The Dynamics of the 2-D Piecewise Tinkerbell Map

Abstract

We  introduce a new map we  call it a Piecewise Tinkerbell , we will prove some general properties of  it, also we study the type of fixed points with respect of the parameter spaces. We prove it has positive  Lypaunov exponents. We search the chaotic of Piecewise Tinkerbell by use the Wiggins’s definition ,we show that the Piecewise Tinkerbell map has  sensitive depends on initial condition by using the software (Matlab). Finally we investigate  transitivity of it by varying the parameter of map.

Keywords: The Piecewise Tinkerbell Map, Sensitive Depends on Initial Condition, Topological Transitive  Map, Lyapunov exponents .